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Abstract: The Blackwell-MacQueen description of sampling from a Dirichlet random distribution on an abstract space is reviewed, and extended to a general family of random discrete distributions. Results are obtained by application of Kingman's theory of partition structures. 1 Introduction Blackwell and MacQueen [10] described the construction of a Dirichlet prior distribution by a generalization of P'olya's urn scheme. While the notion of a random discrete probability measure governed by a Dirichlet... (Update)
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...2 N. Then the sequence X is exchangeable and corresponds to the Dirichlet measure with parameter distribution . As it was shown in [K] [P2], the constructions leading to random Dirichlet measures admit natural generalizations. We now describe a generalized Chinese restaurant...
...defined by (5) for independent beta(1; variables V i , is commonly known as GEM( after Griffiths, Engen and McCloskey. See [8, 13, 21, 24] for background. Theorem 2 combined with Lemma 4 immediately yields the following result, part (i) of which is due to Gnedin Kerov...
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BibTeX entry: (Update)
J. Pitman. Some developments of the Blackwell-MacQueen urn scheme. In T.S. Ferguson et al., editor, Statistics, Probability and Game Theory; Papers in honor of David Blackwell, volume 30 of Lecture Notes-Monograph Series, pages 245--267. Institute of Mathematical Statistics, Hayward, California, 1996. http://citeseer.ist.psu.edu/pitman96some.html More
@misc{ pitman96some,
author = "J. Pitman",
title = "Some developments of the Blackwell-MacQueen urn scheme",
text = "J. Pitman. Some developments of the Blackwell-MacQueen urn scheme. In T.S.
Ferguson et al., editor, Statistics, Probability and Game Theory; Papers
in honor of David Blackwell, volume 30 of Lecture Notes-Monograph Series,
pages 245--267. Institute of Mathematical Statistics, Hayward, California,
1996.",
year = "1996",
url = "citeseer.ist.psu.edu/pitman96some.html" }
Citations (may not include all citations):169 Mixtures of Dirichlet processes with applications to Bayesia.. (context) - Antoniak - 1974
168 A Bayesian analysis of some nonparametric problems (context) - Ferguson - 1973
103 Ferguson distributions via P'olya urn schemes (context) - Blackwell, MacQueen - 1973
67 Concepts of independence for proportions with a generalizati.. (context) - Connor, Mosimann - 1969
44 A constructive definition of Dirichlet priors (context) - Sethuraman - 1994
42 The two-parameter Poisson-Dirichlet distribution derived fro.. - Pitman, Yor - 1995
36 the frequency of numbers containing prime factors of a certa.. (context) - Dickman - 1930
35 Prior distributions on spaces of probability measures (context) - Ferguson - 1974
34 Ordered cycle lengths in a random permutation (context) - Shepp, Lloyd - 1966
32 Arcsine laws and interval partitions derived from a stable s.. (context) - Pitman, Yor - 1992
30 Exchangeability and related topics (context) - Aldous - 1985
26 the asymptotic behavior of Bayes estimates in the discrete c.. (context) - Freedman - 1963
26 Size-biased sampling of Poisson point processes and excursio.. (context) - Perman, Pitman et al. - 1992
24 Random discrete distributions (context) - Kingman - 1975
19 Random discrete distributions invariant under size-biased pe.. - Pitman - 1996
18 Exchangeable and partially exchangeable random partitions (context) - Pitman - 1995
18 Poisson process approximations for the Ewens sampling formul.. (context) - Arratia, Barbour et al. - 1992
17 Exchangeability and the evolution of large populations (context) - Kingman - 1982
17 Polya trees and random distributions (context) - Mauldin, Sudderth et al. - 1992
16 Convergence of Dirichlet measures and the interpretation of .. (context) - Sethuraman, Tiwari - 1982
15 Partition structures derived from Brownian motion and stable.. - Pitman - 1992
14 The representation of partition structures (context) - Kingman - 1978
12 Population genetics theory -- the past and the future (context) - Ewens - 1988
11 Fleming-Viot processes in population genetics (context) - Ethier, Kurtz - 1993
11 Continuity and weak convergence of ranked and size-biased pe.. (context) - Donnelly, Joyce - 1989
11 Order statistics for jumps of normalized subordinators (context) - Perman - 1993
10 Order statistics for decomposable combinatorial structures (context) - Hansen - 1994
10 Estimating the number of species: A review (context) - Bunge, Fitzpatrick - 1993
10 Tailfree and neutral random probabilities and their posterio.. (context) - Doksum - 1974
9 The stationary distribution of the infinitely-many neutral a.. (context) - Watterson - 1976
9 The sampling theory of selectively neutral alleles (context) - Ewens - 1972
9 A model for the distribution of individuals by species in an.. (context) - McCloskey - 1965
8 a constant arising in the theory of symmetric groups and on .. (context) - Ignatov - 1982
8 The relation between the number of species and the number of.. (context) - Fisher, Corbet et al. - 1943
8 Some new tools for Dirichlet priors (context) - Diaconis, Kemperman - 1995
8 Discreteness of Ferguson selections (context) - Blackwell - 1973
7 Coherent random allocations and the Ewens-Pitman formula (context) - Kerov - 1995
7 The asymptotic distribution of factorizations of natural num.. (context) - Vershik - 1986
6 The sampling theory of neutral alleles and an urn model in p.. (context) - Hoppe - 1987
6 Contributions to the theory of Dirichlet processes (context) - Korwar, Hollander - 1973
6 Stochastic Abundance Models with Emphasis on Biological Comm.. (context) - Engen - 1978
6 the asymptotic distribution of large prime factors (context) - Donnelly, Grimmett - 1993
5 Diversity as a concept and its implications for random commu.. (context) - Patil, Taillie - 1977
5 Asymptotic behavior of Bayes estimates (context) - Fabius - 1964
5 The cycle structure of random permutations (context) - Arratia, Tavar'e - 1992
5 Size-biased filtering of Poisson-Dirichlet samples with an a.. (context) - Hoppe - 1986
4 Limit measures arising in the theory of groups (context) - Vershik, Shmidt - 1977
4 Probabilistic bounds on the coefficients of polynomials with.. (context) - Pitman - 1996
4 Canonical representations and convergence criteria for proce.. (context) - Kallenberg - 1973
3 P'olya-like urns and the Ewens sampling formula (context) - Hoppe - 1984
3 To appear in Multivariate Discrete Distributions edited by N (context) - Ewens, Tavar'e et al. - 1995
3 Limit measures arising in the theory of symmetric groups (context) - Vershik, Shmidt - 1978
3 The infinitely-many-neutral-alleles diffusion model (context) - Ethier, Kurtz - 1981
3 Convergence to Fleming--Viot processes in the weak atomic to.. (context) - Ethier, Kurtz - 1994
3 the field of combinatory analysis (context) - Goncharov - 1962
3 The distribution of the frequencies of age-ordered alleles i.. (context) - Ethier - 1990
2 Some useful properties of the Dirichlet process (context) - Rolin - 1992
2 Random alms (context) - Halmos - 1944
2 Sampling theory of the negative binomial and logarithmic ser.. (context) - Anscombe - 1950
2 the distribution of large prime factors (context) - Billingsley - 1972
1 Dirichlet processes produce discrete measures: an elementary.. (context) - Berk, Savage - 1979
1 the distribution of jumps of the Dirichlet Process (context) - Rolin - 1993
1 Species sampling models (context) - Pitman - 1995
1 Refined approximations for the Ewens sampling formula (context) - Barbour - 1992
1 The number of cycles associated with the elements of a permu.. (context) - Greenwood - 1953
1 permutations and the structure of the yule process with immi.. (context) - Joyce, Tavar'e - 1987
1 A canonical representation of symmetrically distributed rand.. (context) - Kallenberg - 1973
1 Nonparametric Bayes estimation of the probability of discove.. (context) - Tiwari, Tripathi - 1989
1 On symmetrically distributed random measures (context) - Kallenberg - 1975
1 Laboratoire Bordelais de Recherche en Informatique (context) - Kerov, Technical - 1996
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